Since the first commercial oil well was drilled in Pennsylvania by Colonel Drake in 1859, more than two million wells have been completed in the United States for the production of crude oil and natural gas. While most of these wells have now been abandoned, American Petroleum Institute records currently indicate that by the end of 1985 there were approximately 880,000 producing hydrocarbon wells still operating within the territorial limits of our nation. Unfortunately, most of these wells are now marginal producers due to their natural production decline, and will soon be abandoned as they become unprofitable to operate. Thus, to satisfy its increasing demand for energy, America has no choice but to locate and develop additional petroleum reserves each year. Since most readily accessible reserves have previously been developed, however, new production can now only be obtained at great risk and expense to the operator. This same general trend of declining production and escalating expense prevails throughout the free-world today.
With these facts in mind, the importance of obtaining maximum production efficiency from every available well site becomes increasingly more apparent with the passage of time. Since hydrocarbons are essentially a non-renewable resource, the world's total supply of available energy is greatly dependent upon the operator's ability to establish and maintain a positive incOme stream from each existing well site. Once a well has been completed, its economic life will thereafter be determined by its ability to produce hydrocarbons at a profit. When operating expenses exceed production revenues, most wells will be plugged and abandoned even though they are perfectly capable of producing additional reserves under pump. By increasing the efficiency of such pumping operations, the commercial life of a typical well can usually be extended for many years to economically extract additional reserves from the ground. In many situations the additional reserves that may be obtained by optimization of the pumping process will comprise a substantial share of the ultimate production potential of a well. Such optimization is especially important for stripper wells that, by definition, produce less than 10 barrels of oil per day, since the expense of operating such wells typically offsets a substantial share of the resulting production revenue.
Most wells are currently drilled by high-speed rotary methods that utilize special drilling fluids to lubricate and cool the drill bit, circulate cuttings out of the hole and control naturally occurring formation pressures. During the course of drilling, one or more tests are typically conducted to measure the fluid content, pressure, temperature and/or productivity of each zone of interest. Open hole logs and drill-stem tests are frequently run, and cores may be taken of some intervals, to determine matrix composition, porosity, permeability and hydrocarbon saturation.
Once a well has been drilled and tested, the well-bore is typically lined with one or more strings of heavy steel casing to prevent the hole from collapsing under pressure. A section of casing is then cemented in place by pumping a high-strength cement slurry down its interior and circulating it back towards the surface through cementing ports to fill a portion of the annulus between the well-bore and the liner. Various known methods, including cementing packers and staged cementing, are frequently used to keep the cementing materials from contacting and infiltrating the most productive reservoirs. By completing a well in this manner, the casing and cement also serve to shut-off the flow of unwanted water into the well from porous formations that lie above or below the productive zones of interest.
After the well has been cased and cemented, the liner is perforated at selected locations to allow for the entry of desired formation fluids. This operation is typically accomplished by means of explosive charges. Abrasive jets of pressurized sand and liquid are sometimes used to establish communication with the formation, and open-hole completion techniques eliminate the need for such operations by keeping both casing and cement away from the formation altogether.
Following perforation of the casing, artificial stimulation of each productive interval is typically required to enhance the rate of fluid entry into the well-bore. If the formation is composed of sandstone, stimulation is usually accomplished by pumping large volumes of viscous fluids into the reservoir under pressure to hydraulically fracture the formation matrix. Such an operation typically creates a large vertical fracture that extends outward from the casing, although in some situations this fracture will be horizontal, depending on the weight of overburden. To prevent the flow channel from closing once the treating pressure has been removed, a propant (usually coarse sand or spherical ceramic balls) is pumped into the formation during this process to hold the fractured formation walls apart. Limestone formations, unlike sandstone, are typically stimulated by pumping large volumes of acid into the matrix under pressure to create a maze of permeable flow channels that extend outwardly from the casing for a considerable distance into the formation.
Once artificially stimulated, a well is ready to be completed into a tank or pipeline. This is done by equipping the well with the necessary downhole and surface equipment for the removal of formation liquids from the casing. Although many wells have sufficient reservoir pressure to flow naturally to the surface, most require the use of a downhole pump to mechanically lift both water and oil above ground. Several basic types of pumps are employed for this purpose, including positive displacement reciprocating pumps, electrically operated downhole submersible pumps, rotary screw pumps, and gas or hydraulically operated plunger lift or jet velocity systems. Because conventional surface mounted pumping units are of simple and rugged design, most wells are currently equipped with this type of equipment that converts the rotating motion of an electric motor or gas/diesel engine into a reciprocating up and down motion. This motion is used to activate a piston pump that is located downhole near the end of a string of production tubing. The downhole piston pump typically has a single acting ball check valve known as the "standing valve" located within the lower inlet side of a polished steel or brass cylinder called the "barrel". Contained within the upper portion of this barrel is a moving check valve known as the "traveling valve", which is actuated from the surface by a string of "sucker rods" that connect the valve to the pumping unit. To prevent fluid from leaking back to its suction side, the traveling valve is often equipped with a plurality of "valve cups" which seal the clearance between the traveling valve and the working barrel. These cups are made out of nylon, leather or other pliable composition materials, and require periodic replacement together with the polished balls and seats when they become worn or corroded. Metal-to-metal piston pumps operate essentially the same, but do not make use of valve cups; instead, they rely on a very small clearance between the polished metal plunger and cylinder to restrict the bypass of liquid.
A second type of downhole pump which is currently used on a small percentage of U.S. and foreign wells is the "electric submersible pump". This pump consists of a multistage centrifugal pump assembly in combination with a high-efficiency electric motor that is attached to the end of the string of production tubing. The only surface equipment required for this type of installation is a motor control panel that regulates power applied to the downhole motor by means of electric wires that are run downhole with the tubing string and pump. These pumps are used for high volume applications, and are quite expensive to install and operate. In such installations all downhole electric equipment is cooled by the fluids that are pumped.
Gas and hydraulic plunger lift systems require the use of high-pressure pumping equipment located above ground, and a free traveling plunger located within the tubing string that is periodically pumped to the surface to purge the tubing of formation liquids. Once the plunger reaches the wellhead, it is then allowed to free-fall back to bottom in preparation for the next operating cycle. Rotary screw pumps, on the other hand, utilize the rotating motion of an aboveground motor that drives the sucker rod string to turn a polished steel mandrel within a rubber stator fixed to the bottom of the tubing. This rotary screw motion "squeezes" liquid to the surface, and is quite efficient when used at depths of less than 2000 feet. Other pumping means utilize the lifting action of a high-velocity stream of pressurized gas or liquid injected into the tubing at formation depth to cause fluid to flow continuously to the surface by means of a pressure or density gradient.
Turning now to the dynamics of well performance, it is important to realize that a producing well is essentially a low pressure region that has been artificially introduced into a naturally occurring geologic reservoir for the purpose of removing resident formation fluids such as water, oil and natural gas. By maintaining the well-bore at a hydrostatic pressure lower than the prevailing reservoir pressure, formation fluids will continuously flow into the bore hole at a rate that is essentially proportional to the established pressure differential between formation and casing. For production to be sustained, casing fluids must be continually removed and transported to either surface tanks or pipelines by natural or artificial means to prevent the bore hole pressure from returning to equilibrium with the reservoir.
Initially, many wells have sufficient bottom hole pressure to flow naturally to the surface without the assistance of mechanical pumping means; these wells are said to exhibit "artesian flow". As reservoir pressures become depleted with time, however, all wells eventually require mechanical pumping means to lift formation liquids to the surface. Since the reciprocating piston pump is the type of equipment most commonly used for this purpose, the discussion that follows is primarily directed towards those applications that make use of this class of hardware. The ensuing comments should be considered generic in nature unless otherwise stated, however, since the same operating characteristics and problem areas will typically be observed with any other type of mechanical pumping equipment.
Most wells produce a combination of water, oil and natural gas, together with a small amount of solid particular contaminants that are transported into the well-bore by the stream of flowing fluids. Such materials will only flow into the casing when the hydrostatic pressure of liquid and gas contained there is reduced below the naturally occurring or artificially enhanced formation pressure. For the purpose of this discussion it will be assumed that all transported solid contaminants remain in suspension within the column of produced liquids, and that the total volume of such contaminants is small relative to the total volume of flowing liquids. It will also be assumed that this mixture of solids and liquids behaves exactly the same as a column of pure water and oil, from a fluid mechanics standpoint, and that all completed zones are commingled and serviced by a common downhole pump.
Whenever a well is completed to simultaneously produce from more than one production interval, the total rate of fluid entry into the casing is governed by the individual rates of fluid entry from each completed reservoir. From a theoretical standpoint, the instantaneous rate of fluid entry into the casing from any one reservoir is a function of many variables such as formation pressure "P.sub.f ", casing pressure "P.sub.c ", reservoir permeability "H", fluid viscosity "V" and flowing surface area "A" of the stimulated formation. For compressible fluids such as natural gas and condensate, the equation which relates these variables to describe the daily fluid entry rate can be quite complicated depending on the actual pressures and temperatures involved. For relatively incompressible liquids such as water and oil, however, the combined fluid entry rate "Q.sub.F " of both liquids may be described with reasonable accuracy over a wide range of operating conditions by the following mathematical expression that is derived from the Darcey Equation for laminar flow: EQU Q.sub.F =(kA)(H/V)(P.sub.f -P.sub.c) (1)
Since the total instantaneous rate of incompressible fluid entry from any one reservoir is equal to the combined entry rates of water and oil, the correct fluid production factor (H/V) to use in this equation is a function of the absolute viscosities and relative permeabilities of both water and oil contained within the formation. This factor depends on the current saturation level of each liquid, and may be expressed mathematically as (H/V)=(H/V).sub.w +(H/V).sub.o. Although the actual value of (H/V) will change slowly with time as fluid is extracted from the reservoir, its prevailing magnitude is essentially constant at any particular time regardless of the pressure drive established between formation and casing. Likewise, the constant "k" depends only on the units of flow desired, such as gallons per minute (GPM) or barrels of fluid per day (BFPD), and the constant "A" depends only on the naturally occurring reservoir porosity and stimulation techniques utilized. Thus, once a reservoir has been completed, the only factor in equation (1) over which the operator has any day-to-day control is the pressure drive (P.sub.f -P.sub.c). Since the remaining factors (kA)(H/V) are essentially constant and independent of pressure drive, on a daily basis, equation (1) may be rewritten as follows: EQU Q.sub.F =(K)*(P.sub.f -P.sub.c) (2)
When a well is first drilled, its naturally occurring reservoir pressure is typically on the order of 350 psi to 450 psi for every 1000 feet of depth below ground level, although significantly greater pressure gradients may frequently be encountered. If several productive zones are encountered, each zone usually has its own reservoir pressure which depends only on the depth and content of that particular formation. During the initial period of "Primary Recovery", the natural pressure of each producing interval declines exponentially with time as fluids are extracted by the natural pressure drive (P.sub.f -P.sub.c). This means that the fluid entry rate "Q.sub.F " into the casing from each zone also declines exponentially with time. Following the natural depletion of any reservoir, its remaining formation pressure may then be artificially enhanced by the introduction of repressuring agents such as water, carbon dioxide or nitrogen to allow for the continued production of hydrocarbons during a period of "Secondary Recovery".
From the above discussion it should be obvious that the total rate of fluid entry into a well is equal to the summation of the individual fluid entry rates "Q.sub.F " from each zone completed. Although each formation may have its own reservoir pressure "P.sub.f ", production factor (H/V) and flowing surface area "A", their individual fluid entry rates are all governed by the same basic equation (1) presented above. This equation indicates that the total fluid production rate "Q.sub.F " obtained from each producing interval is proportional to the pressure drive (P.sub.f -P.sub.c) established across that formation. Thus, to achieve the greatest total rate of fluid entry into the casing for any given set of reservoir conditions, it is only necessary to reduce the hydrostatic pressure within the casing to the lowest value possible. This may be accomplished by pumping all of the liquid from the casing, and by keeping the casing gas pressure as low as possible.
It is important to note that the casing pressure "P.sub.c " which affects fluid entry rate "Q.sub.F " is equal to the arithmetic sum of the casing gas pressure at wellhead plus the hydrostatic pressure of contained liquids at formation depth. Since casing gas is either vented to atmosphere or delivered into the pipeline, the required wellhead gas pressure is usually fixed by marketing considerations over which the operator has very little control. Thus, by removing all liquids from the casing, the greatest production is achieved for any specified gas delivery pressure. Whenever water and oil are allowed to accumulate above the productive interval, the actual rate of fluid entry into the casing is less than optimum since the pressure drive (P.sub.f -P.sub.c) is reduced by the combined hydrostatic head of these liquids. Since the ratio of oil and gas production to total fluid production (i.e. "oil cut" and "gas/oil ratio") remains essentially constant, the total daily production of hydrocarbons will also be less than optimum whenever liquids are allowed to accumulate within the casing.
Except in instances of an artesian well, the maximum rate that fluid can be removed from the casing is controlled by the capacity of the pumping equipment installed. This capacity "Q.sub.p " may be computed as the theoretical displacement of the downhole pump multiplied by the overall volumetric efficiency of all associated downhole equipment. Thus, if a particular downhole pump has a displacement of 200 BFPD, and if it operates at 80% volumetric efficiency as observed on the surface, then its actual pumping rate "Q.sub.p " into the tank or pipeline will be 160 BFPD. This rate is the combined pumping rate for all incompressible fluids being transported, and assumes that a full head of liquid is available to the suction inlet on each successive stroke or revolution of the pump. The actual pumping capacity of any centrifugal, rotary screw or piston pump may be computed as follows: EQU Q.sub.p =(Displacement)*(Volumetric Efficiency) (3)
For purposes of this discussion, the physical displacement of any mechanical pump installation is considered to be a function only of its geometry and speed of operation, and is not dependent on such factors as rod stretch or internal fluid leakage. These inefficiencies, together with all other factors which affect the net production efficiency of a well, are conveniently grouped together and accounted for under the general heading of "overall volumetric efficiency". This efficiency is defined as "The ratio of actual fluid delivery rate to the surface, divided by the theoretical volumetric displacement of the downhole pump", and has nothing to do with the overall thermodynamic efficiency of surface equipment from a mechanical or electrical standpoint.
Whenever fluid is sucked into a downhole pump, its volumetric efficiency is first reduced by the effects of viscosity, friction and inertia that combine to restrict the entry of fluid into the suction chamber. Typically this "suction efficiency" is near 100% for mechanical pumps operating at slow pumping speeds, and decreases as the pumping speed is increased. As the fluid level within the casing is lowered, suction efficiency continuously declines since there is progressively less hydrostatic pressure at the pump inlet to drive liquid past the standing valve and into the pumping chamber. This decline typically is on the order of a few percentage points, and is essentially linear with time. When all stored water is finally depleted from within the casing, the suction efficiency will further decline by a few additional percentage points as the pump begins to ingest the pad of high viscosity oil that floats on top of the water. This last change is rather abrupt since the water/oil interface within the casing is quite well defined. The importance of these two slight but perceptible changes in the overall volumetric efficiency of downhole pumping equipment will be more fully described hereinafter.
Once in the chamber of a piston pump, liquid must first pass through the traveling valve on its downstroke before it can be lifted towards the surface on the following upstroke. During this fluid charging period, the hydrostatic pressure of liquids within the tubing string will be supported by the standing valve, which typically leaks some fluid back into the casing due to an imperfect seal between its ball and seat. Throughout the following upstroke, the weight of liquid transfers to the traveling valve, and some fluid will then leak past the cups or metal plunger and the seated traveling ball to return to the suction side of the valve. Rod stretch reduces piston travel to less than the input stroke of surface equipment, and small leaks in the tubing joints allow pressurized liquid to return to the casing rather than being pumped to the surface. All told, the combination of these various factors work together to reduce the overall volumetric efficiency of all downhole pumping equipment below the theoretical limit of 100%.
Based on the above definition of volumetric efficiency, the theoretical capacity of any reciprocating piston pump may be readily calculated since its mechanical displacement then becomes a simple function of pump diameter, stroke and frequency of operation. Initially, the volumetric efficiency of this type of equipment is typically on the order of 80-95% depending on the particular application and equipment configuration involved. With time, this efficiency declines significantly as the various mechanical components wear with use. At times, this degradation can be quite rapid due to the effect of sand or other contaminants flowing through the pump, and sucker rod failure or large tubing leaks will usually result in the immediate cessation of fluid being transported to the surface. The continuous operation of such equipment without a full head of liquid available to its inlet also causes a rapid degradation of performance since the metal plunger or traveling valve cups are then not properly lubricated. Most of these same factors also affect the performance of centrifugal or rotary screw pumps, which have a theoretical capacity that is similarly determined by their physical geometry and speed of operation. Because of these considerations, the actual volumetric efficiency of a downhole pump is rarely known with any degree of accuracy once such equipment has been operated for any length of time.
It is a common misconception that a downhole piston pump will only move fluid to the surface on the upstroke. This assumption is not always correct, as confirmed by strip-chart recordings (made with the assistance of the herein disclosed invention) of the instantaneous fluid exit rates from many pumping wells that have ranged in depth from 600 to 7600 feet. It is of particular interest to note that this erroneous assumption actually provided the design basis for some prior art motor control devices that reportedly operate based upon the detection of fluid "pump-off".
In order to understand why a piston pump can displace fluid to the surface on both the upstroke and the downstroke, it is only necessary to study the geometry of the working barrel and tubing string when the polish rod, sucker rods and traveling valve are at their maximum and minimum vertical limits of travel. It will first be noted that when the polish rod is at the upper limit of its stroke, there exists within the working barrel a volume of liquid that will soon be displaced through the traveling valve as it makes its downward stroke. Assuming that the well is not "pumped-off", this volume of fluid is very nearly equal to the cross-sectional area of the working barrel multiplied by the length of the pumping stroke. Once on top of the traveling valve, however, this same volume of liquid must occupy a greater height within the working barrel since the cylinder volume above this valve is now reduced by the volume of the sucker rods which actuate said valve. The net effect of this change in geometry is that fluid is usually displaced upward within the tubing string by the downstroke of the traveling valve.
With regard to the capacity of the tubing string in the vicinity of the wellhead, it can be seen that at the top of the upstroke there exists a section of tubing whose liquid volume may be calculated as the volume of tubing less the volume of sucker rods based upon their respective cross sectional areas multiplied by the length of the pumping stroke. On the downstroke, the volume of sucker rods within this upper section of tubing is replaced by the greater volume of the polish rod, which typically has a larger diameter than the rod string. Thus, on the downstroke of the pump, the polish rod acts to displace an additional volume of liquid to the surface. In similar fashion, this displacement acts in reverse on the upstroke to reduce the net volume of fluid exiting the wellhead.
The net effect of both displacements mentioned above is additive, and is offset somewhat by the fact that as fluid exits the working barrel into the tubing string at downhole pump elevation, there exists a slight reduction in the average upward velocity of liquid within the tubing since it is typically of larger diameter than the working barrel. Of further influence are the effects of leakage past the traveling and standing valves during the up and down strokes respectively, and the effects of possible leakage through a plurality of tubing joints When all such displacements and inefficiencies are taken into account, it is frequently found that the typical downhole piston pump installation moves a considerable portion of its total pump capacity to the surface on the downstroke. Many wells, in fact, actually move more fluid on the downstroke than on the upstroke, depending on the physical dimensions and efficiencies of the particular equipment involved.
Whenever formation fluids enter the casing under optimum production conditions, the hydrostatic pressure acting upon these liquids is greatly reduced below the reservoir pressure "P.sub.f ". Because of this, gaseous hydrocarbons originally dissolved within the water and oil come out of solution and physically separate from the other constituents in accordance with their natural order of densities. Water, being the heaviest, falls immediately to the bottom of the well where it accumulates and eventually enters the pump first. Oil, being lighter, rises to float on top of the water and gas, being the lightest, rises to fill the remainder of the casing between liquid interface and wellhead.
Once inside the casing, the amount of gas that remains in liquid solution is dependent only upon the absolute pressure and temperature of the casing fluids at formation depth. If the wellhead gas pressure is not very high, then the gas pressure acting upon the fluid interface at the bottom of the hole will be essentially the same as the gas pressure measured at the surface. Due to the greater densities of water and oil, however, the hydrostatic pressure within each column of liquid increases linearly with depth below the gas/liquid interface. Thus, the amount of gas in solution within the combined liquid column also increases significantly with increasing depth of liquid accumulation. If, for example, casing gas is maintained at a pressure of 100 psig at the wellhead in order to deliver regulated gas into the pipeline, and if liquid is allowed to build within the casing to a height of 500 feet above the pump inlet before such equipment is actuated, then the initial hydrostatic pressure acting upon this column of liquid increases uniformly from 100 psig at the liquid surface to 300 psig at the pump inlet, assuming an average liquid pressure gradient of 0.40 psig per foot of depth. In this case the first liquid ingested into the pump will contain natural gas in solution at a pressure of 300 psig, and the last liquid ingested into the pump just prior to "pump-off" will contain natural gas in solution at a pressure of 100 psig.
Throughout the pumping cycle, liquid is sucked into the pump and discharged on top of the traveling valve, where the hydrostatic pressure within the tubing string is directly related to its setting depth below ground level. If the pump is located 5000 feet below the surface, for instance, then hydrostatic pressure within the tubing is approximately 2000 psig at pump elevation. At this pressure, the gas contained within the liquid column can not possibly come out of solution since it has previously out-gassed to a saturation pressure of between 100 and 300 psig as previously described. As this liquid is pumped to the surface, however, the hydrostatic pressure within the tubing string decreases by approximately 40 psig for every 100 feet of vertical rise; thus, when the first liquid ingested by the pump comes to within 700 feet of the surface, its hydrostatic pressure will have decreased to 300 psig assuming that the wellhead discharge pressure is 20 psig. As the liquid continues to rise above this depth, its hydrostatic pressure further decreases and gas begins to expand out of the super-saturated liquid. This escaping gas continues to expand as it approaches surface elevation, causing the liquid to "flow in head" or surge into the lead line. A similar out-gassing of all additional liquid ingested by the pump likewise occurs in this example at depths ranging from 700 to 200 feet below ground level, where the hydrostatic tubing pressure declines below the minimum casing saturation pressure of 100 psig.
This normal escapement and expansion of dissolved gas within the tubing string chills the liquid and increases its volume as it approaches and finally exits the wellhead. Such expansion causes paraffin to congeal within the tubing, and also causes the apparent volumetric efficiency of the downhole pump to increase since the final volume of separated gas and liquid exiting the wellhead is much greater than the original volume of gas-saturated liquid ingested at the pump inlet. By using a conventional fluid back-pressure valve in the liquid discharge line at the wellhead, as hereinafter disclosed, the hydrostatic liquid discharge pressure can be maintained greater than the greatest possible pump inlet pressure to avoid such problems.
When a well first starts to pump after being shut-down for a certain length of time, there is usually an excess reserve of liquid contained within its casing. Since the pump initially has plenty of liquid available to its inlet, fluid first exits the wellhead at an average rate that is identically equal to the pumping rate "Q.sub.p " of downhole equipment. As the fluid level within the casing is reduced by pumping, additional liquids enter from the formation at an increasing rate that is determined solely by the changing pressure drive (P.sub.f -P.sub.c). Should the available fluid entry rate "Q.sub.F " be greater than the established pumping rate "Q.sub.p ", the hydrostatic casing pressure will eventually decline sufficiently to cause new liquids to enter at a rate that is identically equal to the pumping rate (i.e. Q.sub.F =Q.sub.p). Once equilibrium has been established, no further change in the average casing fluid level will occur except as dictated by a gradually changing reservoir pressure, or by a change in the actual pumping rate due to a degradation of the overall pumping efficiency. If the established pumping rate "Q.sub.p " is greater than the maximum available fluid entry rate "Q.sub.F ", however, then the well will eventually "pump-off" when the pump's initial reserve of liquid is depleted from the casing. Following such event, the average rate of liquid exiting the wellhead can thereafter be no greater than the average rate of new fluids entering the casing from the formation. Accordingly, the energy expended by the prime mover will be inefficiently utilized by the downhole pump if it continues to operate after fluid "pump-off".
Regardless of the type of mechanical pumping equipment used, the downhole pump can be severely damaged if it is operated for any appreciable length of time without a substantial head of liquid available to its inlet. If a piston pump depletes all of the liquid from the casing, for instance, it will thereafter operate in a condition referred to as "fluid pounding" wherein there is insufficient liquid available to the pump on its suction stroke to completely fill the pump barrel with liquid. Under such conditions the pump barrel fills partially with gas, and heavy shock loads are then developed on each successive downstroke as the traveling valve abruptly slams into the liquid interface. These shock loads tend to unscrew the sucker rods which are typically screwed together in 25 feet lengths, thereby causing rod separation that requires a time consuming and expensive "fishing job" to repair. Also, without a substantial charge of liquid passing through the pump on each stroke, wear on the traveling valve cups or metal plunger is accelerated due to insufficient lubrication and the tendency for sand and other solids to precipitate out of the fluid stream. The resulting shock loads due to fluid pounding are also very detrimental to the structural integrity of surface pumping equipment.
In similar fashion, when a downhole submersible pump depletes all of the liquid from the casing, it will thereafter operate at reduced efficiency due to the effects of cavitation induced by the ingested gas. Not only does the pump motor receive insufficient cooling, but the centrifugal pump vanes can be severely damaged by shock loads induced by the collapse of gas bubbles as they travel through the pump. The rubber stator and polished metal mandrel of a rotary screw pump can also suffer similar damage if not operated with a full head of liquid available to its inlet. Sustained fluid pounding also tends to prematurely wear out the stuffing box seals as a result of improper lubrication. This situation will frequently result in a loss of considerable fluid through these worn seals, thereby threatening the adjacent environment and necessitating shut-down of equipment while repairs and clean-up are effected. For these reasons, it is imperative that no type of mechanical downhole pump be operated for any sustained period of time in a severe "pumped-off" condition.
Whenever a downhole mechanical pump is allowed to operate for any length of time in a "pumped-off" condition, the degree of severity of fluid pounding or cavitation is determined by the dimensionless ratio of fluid entry rate "Q.sub.F " divided by the pumping rate "Q.sub.p ". By definition, the fluid entry rate "Q.sub.F " that is used throughout this disclosure shall include any volume of solid particular contaminants that might be suspended within, and transported with, the volume of produced liquids. If the established ratio of "Q.sub.F /Q.sub.p " is just slightly less than 1.0, then the pump receives essentially a full charge of liquid on each suction stroke or revolution, and the effects of fluid pounding or cavitation are almost imperceptible. If the ratio "Q.sub.F /Q.sub.p " is near 0, however, then the pump receives very little liquid in relation to its capacity, and the effects of fluid pounding or cavitation are quite severe. Between these two extremes is a transition zone wherein the detrimental effects of fluid pounding or cavitation become more severe as the ratio "Q.sub.F /Q.sub.p " approaches zero. By contrast, whenever the ratio Q.sub.F /Q.sub.p is greater than 1.0, the well will never "pump-off" inasmuch as fluid can continuously enter the casing at a rate greater than the actual pumping rate of the downhole equipment. Accordingly, in this situation, the production potential of the well will be limited by the capacity of the pumping equipment installed, rather than by the ability of the formation to deliver fluids.
From the above discussion, it should be obvious that the greatest production of oil and gas is obtained at the least operating expense by equipping a well with a downhole pump that has a capacity "Q.sub.p " which is identically equal to the maximum available fluid entry rate "Q.sub.F ". Unfortunately, this result is practically impossible to achieve (and even harder to maintain) in actual practice since both the pumping rate and fluid entry rate of any given well completion will vary considerably from day-to-day due to the effects of changing pump efficiency, reservoir pressure and average fluid viscosity. For this reason, most operators elect to install pumping equipment whose actual volumetric capacity is greater than the maximum available fluid entry rate of the well, and then attempt to control the operating cycle of their prime mover (i.e. electric motor or gas/diesel engine) by the use of a timing device that is manually set to provide for the periodic operation of such equipment. By so doing, the effective pumping capacity of downhole equipment is reduced by the "Duty Cycle" of the prime mover, which is easily controlled from the surface by selecting the desired relationship between "Run Time" and "Rest Time" as follows: EQU Cycle Time=Rest Time+Run Time (4) EQU Duty Cycle=Run Time/Cycle Time (5)
From a theoretical standpoint, the required Duty Cycle of both downhole and surface pumping equipment is equal to the computed value of the dimensionless ratio "Q.sub.F /Q.sub.p ". To derive this relationship, it is convenient to assume that each repetitive operating cycle of the pump will begin at the start of the "rest period" and will end at the conclusion of the following "run period". Under these conditions, the start of each operating cycle is marked by the onset of "fluid pounding" or "cavitation", which begins when the casing liquid level has been reduced to the pump inlet. Since fluid is neither created nor destroyed by the pumping process, and since the inventory of liquids within the casing is always the same at each instant of time when "pump-off" is first reached, "cycle time" and "run time" are closely related to the average values of "Q.sub.F " and "Q.sub.p " as follows: EQU (Q.sub.F)*(Cycle Time)=(Q.sub.p)*(Run Time) (6)
This continuity equation assumes that "Q.sub.F " is essentially constant throughout the entire operating cycle, and further assumes that fluid only exits the casing during periods of actual pump operation. Both of these assumptions are fairly realistic for a properly run well that utilizes a fluid back-pressure valve to minimize the effects of gas expansion in the tubing string, as previously discussed, and that utilizes short rest times to prevent fluid from building excessively within the casing during the rest period. This equation also assumes that fluid exits the wellhead at a constant average rate "Q.sub.p " whenever the downhole pump is actuated by the prime mover, even though such equipment rarely performs in this ideal fashion for reasons hereinafter discussed. By making such an assumption, however, the limiting value of the required duty cycle for both downhole and surface equipment can be readily calculated by combining equations (5) and (6) to yield: EQU Duty Cycle="Q.sub.F /Q.sub.p " (7)
Unfortunately, the actual values of "Q.sub.F " and "Q.sub.p " are rarely known by the operator to any degree of accuracy. Thus, the operator has little choice but to guess at the correct setting for "run time" and "rest time" when programming a conventional timing device, unless he is willing to pay the price to conduct frequent and expensive production tests to measure the average value of "Q.sub.F " and "Q.sub.p " based on actual fluid delivery into a calibrated tank. Also, conventional timing devices are generally programmable only in discrete increments of fifteen minutes or more, which means that accurate selection of the desired duty cycle is not possible in most situations with such equipment.
Even when the correct values of "Q.sub.F " and "Q.sub.p " are accurately known, total fluid production into a tank or pipeline is less than optimum when pumping equipment is controlled by a conventional timing device that is programmed according to the dimensionless ration "Q.sub.F /Q.sub.p ". Such devices, being passive in nature, make no allowance for the transients of initial start-up, or for the fact that selected "rest times" may be inadvertently lengthened, or "run-times" improperly shortened, by unforeseen power interruptions. Such devices additionally make no allowance for the fact that fluid will frequently "fall-back" into the casing during periods of equipment "rest" as the result of leaks in the tubing string or downhole pumping valves, and make no allowance for the transient effects of sand and/or gas that frequently interrupt normal pump operation as they pass through the suction chamber together with formation fluids.
Because of these considerations, the proper selection and regulation of the required duty cycle for any particular well completion is quite difficult to achieve using conventional timing equipment that must be manually programmed by the operator. Accordingly, most wells are either under-pumped or over-pumped to some degree, with an attendant reduction in either fluid production or operating efficiency respectively.
If optimum production is to be maintained by a mechanical pump without the adverse effects of fluid pounding or cavitation, then it is essential that a proper "rest time" be selected for programming into the motor control device that is used to regulate the duty cycle of downhole equipment. This may be clearly understood by considering the fact that the rate of fluid entry (Q.sub.F) into the casing decreases exponentially with time as the available pressure drive (P.sub.f -P.sub.c) diminishes with increasing fluid height. Since the greatest fluid buildup occurs during the first few minutes of liquid accumulation, the average daily fluid entry rate into the casing will be severely affected by the "rest time" selected for its pumping equipment. A well that requires five hours, (i.e., 300 minutes) to accumulate 500 feet of liquid during the "rest period", for instance, will require only 6.2% of this time (i.e., 19 minutes) to accumulate 25% of this volume, and will require only 15% of such time (i.e., 45 minutes) to accumulate 50% of this volume. For this reason, it is imperative that the total daily "rest time" of any pump be limited in duration and uniformly distributed throughout each 24 hour operating period.
The optimum "rest time" for any well is a function of its casing size, tubing size, fluid entry rate, bottom hole pressure, oil cut, gas/oil ratio, fixed overhead expense, energy cost, maintenance expense, pumping rate and certain other factors such as the water disposal cost and prevailing market price for oil and gas production. In general, long "rest times" result in lost production whereas short "rest times" result in excessive maintenance problems due to the frequent cycling of surface and downhole equipment. With few exceptions the optimum "rest time" for any particular well results in a slight but almost imperceptible trade-off of production revenue for a greatly reduced expense of energy consumption and equipment maintenance. "Rest times" on the order of a few minutes to several hours are usually appropriate for most wells, depending on the established value of Q.sub.F /Q.sub.p, although greater intervals may safely be used whenever fluid entry rates are extremely low and/or formation pressures extremely high.
Various types of "pump-off detectors" have been devised over the years to control the operating cycle of a producing well. Some of the most common "pump-off" detection systems utilize a vibration sensor mounted on the Sampson post or gear box of the pumping unit to detect the slight change in system oscillation that normally occurs at the onset of fluid pounding or cavitation. Other systems utilized a strain-gauge mounted on the polish rod, walking beam or pitman arm to detect the change in time-averaged rod loading which results from less fluid being moved to the surface after "pump-off". Solid-state motor current sensors have recently been used to detect the slight reduction in average power output of the prime mover that normally occurs at the onset of fluid pounding or cavitation, and fluid flow switches have been utilized to indirectly detect the change in pumping rate of downhole equipment which occurs when the reserve of liquid is first depleted from within the casing. Certain other devices attempt to avoid "pump-off" altogether by measuring the actual fluid level within the casing; these systems typically operate by means of a downhole float switch mounted on the tubing string immediately above the pump inlet, or by means of a surface generated acoustic signal that is reflected off of the liquid/gas interface within the casing.
Unfortunately, all of the above methods for detecting "pump-off" require that a sensing circuit be accurately calibrated for the specific installation at hand. Fluid switches, for instance, typically operate by detecting a change in the average or peak flow line pressure at the wellhead, or by detecting a change in the average or peak pressure differential across an orifice plate installed in said line. When the average fluid exit pressure (or pressure differential across the orifice plate) decreases below a preselected trigger point, or when the peak pulsating pressure amplitude or pressure differential ceases to rise above this preselected reference point, then the system automatically assumes that "pump-off" has occurred. Selection of the correct trigger point for each application requires that the operator have a detailed knowledge of the pumping characteristics of his well, since the typical "before" and "after" fluid exit pressures (or pressure differentials across the orifice plate) must be known with reasonable accuracy for proper calibration of equipment at time of installation. Similar considerations will also apply to "pump-off" detection systems that operate on the basis of changing rod load, equipment vibration or prime mover power output. Thus, the correct trigger point for each well installation can only be determined by trained engineers or technicians in the field, where conventional "pump-off" detection equipment must be accurately calibrated for each particular set of operating conditions.
Perhaps the greatest deficiency of conventional "pump-off" detection equipment concerns their inability to automatically respond to normal changes in both reservoir and downhole equipment performance. Once a conventional sensing circuit has been calibrated to a specific set of operating conditions, it can thereafter only respond to changes in the measured parameter (i.e. pressure, load, vibration or power) that occur relative to the selected point of reference. Most of these parameters change on a daily basis throughout the operating life of a well, however, and thus frequent recalibration of conventional "pump-off" detection equipment is required for dependable operation.
Still another problem with conventional "pump-off" detection equipment concerns their inability to operate with great sensitivity in situations where the well is operating at a high ratio of "Q.sub.F /Q.sub.p ". As previously discussed, the effects of fluid pounding or cavitation decreases with increasing values of "Q.sub.F /Q.sub.p ", and disappear completely when the well is operated at a ratio of 1.0 or higher. Also, slight changes in the pumping rate of downhole equipment normally occur prior to the initiation of "pump-off" due to the changing level and viscosity of fluids within the casing. Unfortunately, the operator rarely knows the actual operating conditions of his well, and thus he can not depend on conventional equipment to perform properly under all situations. This limitation severely restricts the widespread use and application of conventional "pump-off" detection equipment, regardless of their construction or mode of operation.